메뉴 건너뛰기




Volumn 2, Issue 2, 1996, Pages 155-295

Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001010413     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/BF01587936     Document Type: Article
Times cited : (144)

References (65)
  • 1
    • 24544466960 scopus 로고
    • Thèse de Doctorat January, Université de Paris XI, 91405 Orsay Cedex, France
    • P. Assouad. Espaces Métriques, Plongements, Facteurs. Thèse de Doctorat (January, 1977), Université de Paris XI, 91405 Orsay Cedex, France.
    • (1977) Espaces Métriques, Plongements, Facteurs
    • Assouad, P.1
  • 4
    • 84967735808 scopus 로고
    • Coupling and Harnack inequalities for Sierpinski carpets
    • M. Barlow and R. Bass. Coupling and Harnack inequalities for Sierpinski carpets. Bull. Amer. Math. Soc 29 (1993), 208-212.
    • (1993) Bull. Amer. Math. Soc , vol.29 , pp. 208-212
    • Barlow, M.1    Bass, R.2
  • 5
    • 0039564331 scopus 로고
    • On Hausdorff-Gromov convergence and a theorem of Paulin
    • M. Bridson and G. Swarup. On Hausdorff-Gromov convergence and a theorem of Paulin. L'Enseignement Mathématique 40 (1994), 267-289.
    • (1994) L'Enseignement Mathématique , vol.40 , pp. 267-289
    • Bridson, M.1    Swarup, G.2
  • 8
    • 0005541251 scopus 로고
    • The characterization of topological manifolds of dimension n ≥ 5
    • Helsinki
    • J. Cannon. The characterization of topological manifolds of dimension n ≥ 5. Proceedings I.C.M. (Helsinki, 1978), 449-454.
    • (1978) Proceedings I.C.M. , pp. 449-454
    • Cannon, J.1
  • 9
    • 0002439897 scopus 로고
    • Shrinking cell-like decompositions of manifolds: Codimension 3
    • J. Cannon. Shrinking cell-like decompositions of manifolds: codimension 3. Ann. Math. (2) 110 (1979), 83-112.
    • (1979) Ann. Math. , vol.110 , Issue.2 , pp. 83-112
    • Cannon, J.1
  • 11
    • 0003232322 scopus 로고
    • Analyse Harmonique Non-commutative sur Certains Espaces Homogènes
    • Springer-Verlag
    • R. Coifman and G. Weiss. Analyse Harmonique Non-commutative sur Certains Espaces Homogènes. Lecture Notes in Math, 242 Springer-Verlag, 1971.
    • (1971) Lecture Notes in Math , vol.242
    • Coifman, R.1    Weiss, G.2
  • 12
    • 84966261604 scopus 로고
    • Extensions of Hardy spaces and their use in analysis
    • R. Coifman and G. Weiss. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc 83 (1977), 569-645.
    • (1977) Bull. Amer. Math. Soc , vol.83 , pp. 569-645
    • Coifman, R.1    Weiss, G.2
  • 14
    • 0000024241 scopus 로고
    • ∞-weights, Sobolev inequalities, and quasiconformal mappings
    • Analysis and Partial Differential Equations (C. Sadosky, ed.); Marcel Dekker
    • ∞-weights, Sobolev inequalities, and quasiconformal mappings, in Analysis and Partial Differential Equations (C. Sadosky, ed.); Lecture Notes in Pure and Applied Mathematics, 122 Marcel Dekker 1990
    • (1990) Lecture Notes in Pure and Applied Mathematics , vol.122
    • David, G.1    Semmes, S.2
  • 15
    • 84968497861 scopus 로고
    • Quantitative rectifiability and Lipschitz mappings
    • G. David and S. Semmes. Quantitative rectifiability and Lipschitz mappings. Transactions Amer. Math. Soc. 337 (1993), 855-889.
    • (1993) Transactions Amer. Math. Soc. , vol.337 , pp. 855-889
    • David, G.1    Semmes, S.2
  • 16
    • 0000254693 scopus 로고
    • Quasiconformal 4-manifolds
    • S. Donaldson and D. Sullivan. Quasiconformal 4-manifolds. Acta Math. 163 (1989), 181-252.
    • (1989) Acta Math. , vol.163 , pp. 181-252
    • Donaldson, S.1    Sullivan, D.2
  • 18
    • 0001563863 scopus 로고
    • The topology of manifolds and cell-like maps
    • Helsinki
    • R. Edwards. The topology of manifolds and cell-like maps. Proceedings I.C.M. (Helsinki, 1978), 111-127
    • (1978) Proceedings I.C.M. , pp. 111-127
    • Edwards, R.1
  • 19
    • 0001591866 scopus 로고
    • On Novikov's conjecture for non-positively curved manifolds, I
    • F. T. Farrell and W. C. Hsiang. On Novikov's conjecture for non-positively curved manifolds, I. Ann. Math. (2) 113 (1981), 199-209.
    • (1981) Ann. Math. , vol.113 , Issue.2 , pp. 199-209
    • Farrell, F.T.1    Hsiang, W.C.2
  • 22
    • 84974000409 scopus 로고
    • Topological finiteness theorems for manifolds in Gromov-HausdorfF space
    • S. Ferry. Topological finiteness theorems for manifolds in Gromov-HausdorfF space. Duke Math. J. 74 (1994), 95-106.
    • (1994) Duke Math. J. , vol.74 , pp. 95-106
    • Ferry, S.1
  • 25
    • 0000876740 scopus 로고
    • Subelliptic estimates and function spaces on nilpotent Lie groups
    • G. Folland. Subelliptic estimates and function spaces on nilpotent Lie groups. Arkiv f. Mat. 13 (1975), 161-207.
    • (1975) Arkiv F. Mat. , vol.13 , pp. 161-207
    • Folland, G.1
  • 26
    • 84980130284 scopus 로고
    • b-complex and analysis on the Heisenberg group
    • b- complex and analysis on the Heisenberg group. Comm. Pure Appl. Math. 27 (1974), 429-522.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 429-522
    • Folland, G.1    Stein, E.2
  • 27
    • 0003233074 scopus 로고
    • Hardy Spaces on Homogeneous Groups
    • Princeton University Press
    • G. Folland and E. Stein. Hardy Spaces on Homogeneous Groups. Math. Notes 28 (1982); Princeton University Press.
    • (1982) Math. Notes , vol.28
    • Folland, G.1    Stein, E.2
  • 29
    • 0002038388 scopus 로고
    • p integrability of the partial derivatives of a quasiconformal mapping
    • p integrability of the partial derivatives of a quasiconformal mapping. Acta Math. 130 (1973), 265-277.
    • (1973) Acta Math. , vol.130 , pp. 265-277
    • Gehring, F.1
  • 31
    • 84974000736 scopus 로고
    • Little topology, big volume
    • R. Greene and P. Petersen V. Little topology, big volume. Duke. Math. J. 67 (1992), 273-290.
    • (1992) Duke. Math. J. , vol.67 , pp. 273-290
    • Greene, R.1    Petersen V, P.2
  • 32
    • 0000976022 scopus 로고
    • Geometric finiteness theorems via controlled topology
    • erratum 104 (1991), 221-222
    • K. Grove, P. Petersen V, and J.-Y. Wu. Geometric finiteness theorems via controlled topology. Invent. Math. 99 (1990), 205-213; erratum 104 (1991), 221-222.
    • (1990) Invent. Math. , vol.99 , pp. 205-213
    • Grove, K.1    Petersen V, P.2    Wu, J.-Y.3
  • 34
    • 51649160427 scopus 로고
    • Groups of polynomial growth and expanding maps
    • M. Gromov. Groups of polynomial growth and expanding maps. Publ. Math. IHES 53 (1981), 183-215.
    • (1981) Publ. Math. IHES , vol.53 , pp. 183-215
    • Gromov, M.1
  • 35
    • 84956267209 scopus 로고
    • Filling Riemannian manifolds
    • M. Gromov. Filling Riemannian manifolds. J. Differential Geometry 18 (1983), 1-147.
    • (1983) J. Differential Geometry , vol.18 , pp. 1-147
    • Gromov, M.1
  • 36
    • 0002874575 scopus 로고
    • Asymptotic invariants of infinite groups
    • Proceedings of the 1991 conference Sussex conference on Geometric Group Theory, Niblo and Koller, editors, Cambridge Univ. Press
    • M. Gromov. Asymptotic invariants of infinite groups. Proceedings of the 1991 conference Sussex conference on Geometric Group Theory, Niblo and Koller, editors, London math. Soc. Lecture Notes 182 (1993); Cambridge Univ. Press.
    • (1993) London Math. Soc. Lecture Notes , vol.182
    • Gromov, M.1
  • 41
    • 84972555264 scopus 로고
    • The Poincaré inequality for vector fields satisfying Hörmander's condition
    • D. Jerison. The Poincaré inequality for vector fields satisfying Hörmander's condition. Duke Math. J. 53 (1986), 503-523.
    • (1986) Duke Math. J. , vol.53 , pp. 503-523
    • Jerison, D.1
  • 42
    • 0003338950 scopus 로고
    • The Topology of 4-Manifolds
    • Springer-Verlag
    • R. Kirby. The Topology of 4-Manifolds. Lecture Notes in Math, vol. 1374. Springer-Verlag, 1989.
    • (1989) Lecture Notes in Math , vol.1374
    • Kirby, R.1
  • 47
    • 84972499184 scopus 로고
    • A finiteness theorem for metric spaces
    • P. Petersen V. A finiteness theorem for metric spaces. J. Diff. Geom. 31 (1990). 387-395.
    • (1990) J. Diff. Geom. , vol.31 , pp. 387-395
    • Petersen V, P.1
  • 48
    • 0001520920 scopus 로고
    • Gromov-Hausdorff convergence of metric spaces
    • P. Petersen V. Gromov-Hausdorff convergence of metric spaces. Proc. Sym. Pure Math. 54 Part 3 (1993), 489-504;
    • (1993) Proc. Sym. Pure Math. , vol.54 , Issue.3 PART , pp. 489-504
    • Petersen V, P.1
  • 51
    • 4244094624 scopus 로고
    • n (without bounds on their smoothness)
    • n (without bounds on their smoothness). Indiana Math. J. 39 (1990), 985-1004.
    • (1990) Indiana Math. J. , vol.39 , pp. 985-1004
    • Semmes, S.1
  • 53
    • 0002180640 scopus 로고
    • Finding structure in sets with little smoothness
    • Zürich
    • S. Semmes. Finding structure in sets with little smoothness. Proc. I.C.M. (Zürich, 1994), Birkhäuser, 1995, p875-885.
    • (1994) Proc. I.C.M. , pp. 875-885
    • Semmes, S.1
  • 54
    • 85157070788 scopus 로고    scopus 로고
    • Revista Matemática Iberoamericana
    • ∞ weights. Revista Matemática Iberoamericana, 1996.
    • (1996) ∞ Weights
    • Semmes, S.1
  • 61
    • 0001403187 scopus 로고
    • Quasisymmetric embeddings in Euclidean spaces
    • J. Väisälä. Quasisymmetric embeddings in Euclidean spaces. Trans. Amer. Math. Soc. 264 (1981), 191-204.
    • (1981) Trans. Amer. Math. Soc. , vol.264 , pp. 191-204
    • Väisälä, J.1
  • 64
    • 84972539522 scopus 로고
    • On maps of an n-sphere into another n-sphere
    • H. Whitney. On maps of an n-sphere into another n-sphere. Duke Math. J. 3 (1937), 46-50.
    • (1937) Duke Math. J. , vol.3 , pp. 46-50
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.